An astronaut in his space suit and with a propulsion unit (empty of its gas prop

Question

An astronaut in his space suit and with a propulsion unit (empty of its gas propellant) strapped to his back has a mass of 158 kg. During a space-walk, the unit, which has been completely filled with propellant gas, ejects some gas with a velocity of +32 m/s. As a result, the astronaut recoils with a velocity of -0.48 m/s. After the gas is ejected, the mass of the astronaut (now wearing a partially empty propulsion unit) is 165 kg. What percentage of the gas propellant in the completely filled propulsion unit was depleted?

Explanation / Answer

Let mp = the total mass of the propellant in a full propulsion unit. Assuming the gas the astronaut ejected was done so instantly, then the forces (F=m*a) on the ejected propellant and the astronaut are: F(astronaut) = 172 kg * (-0.432 m/s) = -74.304 N F(propellant) = (134 kg + mp - 172 kg) * (34.7 m/s) Because of Newton's 3rd law, the force on the gas is equal and opposite to the force on the astronaut: F(propellant) = -F(astronaut) (mp - 38 kg) * 34.7 m/s = 74.304 N Solving gives mp = 40.1413 kg We also know that the amount of propellant left is 172 - 134 = 38 kg So, the percentage depleted (used) is 100 * (40.1413 - 38) / 40.1413 = 5.33%

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